Download App

4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $(1 - i)^n = 2^n,$ then $n = $
  • A
    $1$
  • ✓
    $0$
  • C
    $- 1$
  • D
    None of these
✓

Answer

Correct option: B.
$0$
b
(b) If $(1 - i)^n = 2^n$ ......$(i)$
We know that if two complex numbers are equal, their moduli must also be equal, therefore from $(i)$, we have
$|(1 - i)^n|\, = \,|2^n|$

$ \Rightarrow $ $|1 - i|^n = \,|2|^n$,$(\because \,\,2^n > 0)$
==> $\left[ \sqrt {{1^2} + {{( - 1)}^2}}  \right]^n = 2^n$

==> $(\sqrt 2 )^n = 2^n$
==> $2^{n/2} = 2^n$

==> $\frac{n}{2} = n$

==>$n = 0$
Trick : By inspection, ${(1 - i)^0} = {2^0}\,\,\,\, \Rightarrow 1 = 1$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\mathop {\lim }\limits_{a \to 0} \frac{{\sin a - \tan a}}{{{{\sin }^3}a}}$ will be
→
The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt 2 $, is
→
The equation whose roots are $\frac{1}{{3 + \sqrt 2 }}$and $\frac{1}{{3 - \sqrt 2 }}$ is
→
If the coefficient of $x ^7$ in $\left(a x-\frac{1}{b x^2}\right)^{13}$ and the coefficient of $x^{-5}$ in $\left(a x+\frac{1}{b x^2}\right)^{13}$ are equal, then $a^4 b^4$ is equal to :
→
The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is:
→
The number of ways in which $6$ rings can be worn on the four fingers of one hand is
→
Three dice are thrown simultaneously. What is the probability of obtaining a total of $17$ or $18$
→
If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in
→
For a frequency distribution $7^{th}$ decile is computed by the formula
→
Let $P$ be an interior point of a convex quadrilateral $A B C D$ and $K, L, M, N$ be the mid-points of $A B, B C$, $C D, D A$ respectively. If Area $(P K A N)=25$, Area $(P L B K)=36$, and Area $(P M D N)=41$ then Area $(P L C M)$ is
→